Selecting$2^{m-p}$Designs Using a Minimum Aberration Criterion When Some Two-Factor Interactions Are Important

We consider the problem of selecting appropriate$2^{m-p}$designs when some two-factor interactions are important. Current methods in the literature select designs that permit estimation of the postulated model consisting of the main effects and important two-factor interactions, under the assumption that all of the other effects are negligible. When the effects not in the postulated model are not negligible, they will bias the estimates of the effects in the model. To minimize the contamination of these nonnegligible effects on the model, we propose and study a minimum aberration criterion. We then discuss the application of this new aberration criterion to compromise plans. Finally, we examine how to search for the best designs according to the criterion and present some results for designs of 16 and 32 runs.